At present, the large-scale development of offshore wind farms and technical and economic advantages of DC power transmission are greatly encouraging the use of MTDC power networks. As a foundation of operation regulation of MTDC power networks, the method for obtaining line-transferred active power flows, especially the accurate and fast and reliable method for obtaining line-transferred linear active power flows is urgently needed to be developed.
The existing methods for obtaining line-transferred active power flows in a MTDC power network are iterative ones based on a system of non-linear equations of buses' injection active powers in terms of buses' voltages. Since the non-linearity of the system of non-linear equations, the existing methods are not only time-consumed in each iteration but also unreliable in convergence. As a result, they are not fast enough and not applicable for real-time operation regulation of simple MTDC power networks (those are the power networks of 3 buses), and especially not applicable for real-time operation regulation of complex MTDC power networks (those are the power networks have more than 3 buses). If the incremental linear models produced by linearizing the existing ones at their basic operation points are adopted, they are indeed applicable for the adjacent areas of their basic operation points but not applicable for widely varying operation states of the MTDC power network. Therefore, the above existing methods for obtaining line-transferred active power flows in MTDC power networks are not only time-consumed and unreliable, but also not fast enough for real-time operation regulation of arbitrarily completed MTDC power networks and not applicable for widely varying operation states of them.